### Converting the Unit from cmHg to Pa

Pressure in unit cmHg can be converted to Pa by using the formulaP = hρg

**Example 1**:

Find the pressure at point A, B, C, D, D, E and F in the unit of cmHg and Pa. [Density of mercury = 13600 kg/m³]

**Answer**:

Pressure in unit cmHg | Pressure in unit Pa |
---|---|

P_{A} = 0P _{B} = 17 cmHgP _{C} = 17 + 59 = 76 cmHgP _{D} = 76 + 8 = 84 cmHgP _{E} = 76 cmHgP _{F} = 76 cmHg | P_{A} = 0P _{B} = hρg = (0.17)(13600)(10) = 23,120 PaP _{C} = hρg = (0.76)(13600)(10) = 103,360 PaP _{D} = hρg = (0.84)(13600)(10) = 114,240 PaP _{E} = hρg = (0.76)(13600)(10) = 103,360 PaP _{F} = hρg = (0.76)(13600)(10) = 103,360 Pa |

**Example 4**:

Figure above shows a mercury barometer whereby the atmospheric pressure is 760 mm Hg on a particular day. Determine the pressure at point

a. A,

b. B,

c. C.

[Density of Mercury = 13 600 kg/m³]

**Answer**:

**a.**

P

_{A}= 0**b.**

P

_{B}= 50 cmHgor

P

_{B}= hρg = (0.50)(13600)(10) = 68 000 Pa**c.**

P

_{C}= 76 cmHgor

P

_{C}= hρg = (0.76)(13600)(10) = 103 360 Pa**Example 6**:

If the atmospheric pressure in a housing area is 100 000 Pa, what is the magnitude of the force exerted by the atmospheric gas on a flat horizontal roof of dimensions 5m × 4m?

**Answer**:

Area of the roof = 5 x 4 = 20 m²

Force acted on the roof

F = PA

F = (100 000)(20)

F = 2,000,000 N

**Example 5**:

Figure above shows a simple barometer, with some air trapped in the tube. Given that the atmospheric pressure is equal to 101000 Pa, find the pressure of the trapped gas. [Density of Mercury = 13 600 kg/m³]

**Answer**:

Pressure of the air = Pair

Atmospheric pressure = Patm

Pair + 55 cmHg = Patm

Pair

= Patm – 55 cmHg

= 101 000 – (0.55)(13 600)(10)

= 101 000 – 74 800

= 26 200 Pa

**Example 7**:

Figure(a) above shows the vertical height of mercury in a mercury barometer in a laboratory. Figure(b) shows the mercury barometer in water at a depth of 2.0 m.

Find the vertical height (h) of the mercury in the barometer in the water. Given that the pressure at a depth of 10 m from the water surface is 75 cmHg. [Density of water = 1000 kg/m³, Density of mercury = 13 600 kg/m³]

**Answer**:

Atmospheric pressure,

P

_{atm}= 75 cmHg

Pressure caused by the water,

P

_{water}= 2/10 x 75 = 15cmHg

Pressure in 2m under water

= 75 + 15 = 90 cmHg

Vertical height of the mercury = 90cm